The geometric sequence $(a_i)$ is defined by the formula: $a_1 = -\dfrac{16}{9}$ $a_i = \dfrac{3}{2}a_{i-1}$ What is $a_{2}$, the second term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $-\dfrac{16}{9}$ and the common ratio is $\dfrac{3}{2}$ The second term is simply the first term times the common ratio. Therefore, the second term is equal to $a_2 = -\dfrac{16}{9} \cdot \dfrac{3}{2} = -\dfrac{8}{3}$.